Radioactive Decay: Are stable elements really stable?

I have been snooping around and what i find is that radioactive decay occurs because of instability of the atom nucleus in quantity, proton-neutron ratio and energy content; therefore we have alpha, beta and gamma decay consecutively.

Therefore highly radioactive elements like Uranium undergo constant decay into less radioactive and more stable elements. Each half-life decay takes longer and longer in a exponential manner; therefore theoretically speaking, it takes forever for any element to completely decay into zero.

Although it explains why radioactive decay occurs on unstable elements or isotopes, it doesn't explain why it occurs on stable elements. Unless, stable elements are not really "stable" but the rate of decay are rather slow and harmless to human beings so we label it "stable."

Then if that is the case, then why elements are always decaying or always "unstable"?
Of course, this just an assumption of mine. Anybody can provide me a more conclusive answer?

'Stable' is synonymous with 'doesn't decay'. Any stable nucleus will not decay. Some elements, like carbon, with 6 protons, have some stable isotopes, with 6 neutrons in this case, and some unstable, with 7 or 8. The reason there's still a proportion of these unstable isotopes in naturally occurring samples is because they're constantly being created by cosmic ray collisions.

henry_m, if you were right; carbon dating would be useless. It is because "stable" carbon still undergo radioactive decay that people are able to measure precisely when certain historical artifacts are from.

Of course, carbon dating does not apply anymore to objects on the surface because nuclear testings messed up the isotopes on the surface. However, carbon dating still works for artifacts buried deep enough into the ground.

Therefore highly radioactive elements like Uranium undergo constant decay into less radioactive and more stable elements.

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Some of Uranium's decay products are more radioactive, not less.

Each half-life decay takes longer and longer in a exponential manner;

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Each half-life decay takes exactly the same amount of time.

Although it explains why radioactive decay occurs on unstable elements or isotopes, it doesn't explain why it occurs on stable elements.

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Stable isotopes do not decay.

henry_m, if you were right; carbon dating would be useless. It is because "stable" carbon still undergo radioactive decay that people are able to measure precisely when certain historical artifacts are from.

Thanks for the remarks. I was trying to imply that the idea of radioactive decay is that atoms are trying to stabilize itself by decaying. Although like you said, sometimes the products are more radioactive.

The decay of a sample of radioactive material is exponential, given by A(t) = A(0)exp(-lambda*t), where lambda is ln(2)/T (T = the half life), but the half life T (the time it takes for a sample to statistcially decay to 1/2 it's original activity) is constant. You can see this for yourself by taking A(t) = 0.5A(0), or 0.5=exp(-lambda*t) and you'll find t = T.

As for carbon-14, it is created by high energy cosmic rays interacting with the stratosphere and troposphere to produce neutrons, which causes the 14N(n,p)14C reaction. The carbon is taken up by living things, and when the creature dies, the rate of uptake ceases. The carbon decays witha half life of about 5715 years. Since the concentration of carbon-14 is relatively constant, we can date when the creature died. It has about a 1 part per trillion concentration in the atmosphere http://en.wikipedia.org/wiki/Carbon-14

"Bi-209 has been known as stable nuclide. But, alpha decay of Bi-209 with a half time of 2*10^19 years was found, recently.
Reference : PIERRE DE MARCILLAC, NOEL CORON, GERARD DAMBIER, JACQUES LEBLANC & JEAN-PIERRE MOALIC, " Experimental detection of a-particles from the radioactive decay of natural bismuth," Nature 422, 876-878 (2003); doi:10.1038/nature01541."

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When I found out about that one I nearly freaked at the calculation just to get enough of the material to produce decay events that could exceed an MDA. Foir just an activity of 1Bq, you need over 300kg!!!